Attaching handles to Delaunay nodo\"{\i}ds

Frank Pacard; Harold Rosenberg

Attaching handles to Delaunay nodo\"{\i}ds

Differential Geometry 2010-10-26 v1

Authors: Frank Pacard , Harold Rosenberg

Abstract

For all $m \in \mathbb N - \{0\}$ , we prove the existence of a one dimensional family of genus $m$ , constant mean curvature (equal to 1) surfaces which are complete, immersed in $\mathbb R^3$ and have two Delaunay ends asymptotic to nodo\"{\i}dal ends. Moreover, these surfaces are invariant under the group of isometries of $\mathbb R^3$ leaving a horizontal regular polygon with $m+1$ sides fixed.

Keywords

Delaunay surfaces constant mean curvature nodoïdal ends attaching handles immersed surfaces

Cite

@article{arxiv.1010.4974,
  title  = {Attaching handles to Delaunay nodo\"{\i}ds},
  author = {Frank Pacard and Harold Rosenberg},
  journal= {arXiv preprint arXiv:1010.4974},
  year   = {2010}
}

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